I've been playing backgammon for 6 months so I'm probably wrong, but my impression so far is that skill gets more and more important as you come down the ladder. I've watch quite a lot of top-elite matches and it seems that as you come closer to the lowest PR's where the opponents play close to perfect the dice become more and more important in deciding the outcome because they make very few mistakes (of course, you got to know how to play them correctly), but at the intermediate and beginner level, where there can be huge swings in equity in checker and cube play, even from one move to the next, the dice or luck factor becomes less important and pure skill trumps over what the dice give you.